You have decided to become a structural engineer who specializes in roller coaster design. Your job is to design your own roller coaster ride. To complete this task, please follow these steps:
The amusement park you are designing for gave you the following coaster requirements:
- your coaster ride must have at least 3 relative maxima and/or minima
- the ride length must be at least 4 minutes
- the coaster ride starts at 750 m
- the ride dives below the ground into a tunnel at least once
- be sure to include at least one of each of the following on your design: one double root (multiplicity of two), at least 2 real root.
1. Draw a rough sketch of your "roller coaster" ride on a coordinate plane.
Note: Be sure to illustrate your x-axis and y-axis scale to identify the length of the ride and the height of the ride you are designing. Make sure your design meets all the criteria listed above. [8 points]
2. List all zeros/roots and their multiplicity of your polynomial. [3 points]
3. Write the complete factored form of your roller coaster polynomial. [3 points]
4. Find a possible equation that represents your roller coaster ride. First in factored form then in standard form [7 points]
5. Assuming your rollercoaster is continuous, describe the end behavior of your function. [2 points]
6. Color the graph blue where the polynomial is increasing and red where the polynomial is decreasing. [2 points]
7. Calculate the speed of your rollercoaster if it stretches across 1,025 meters (based on the time of your rollercoaster from your graph).
Hint: [2 points]
8. Does your rollercoaster design meet all the requirements of the amusement park? Provide at least 3 reasons in your response. [3 points]